Tutorials - Digital Signal Processing: An Introduction with MATLAB and Applications - page 230

u(t)

1

t

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

u(−t)

t

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

u ( t −3) (right shift)

t

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

u (− t −3)= u [−( t +3)] (left shift)

t

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

u(t+5)

t

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

u (− t +5)

t

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

u ( t )

y ( t )= u ( t )− u ( t −1)

t

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

− u ( t −1)

Tutorial 2

Q1: Find the I/O (input-output) relation of the system shown below.

Time−delay, T o

x ( t )
Input
signal

y ( t )
Output
signal

2

Solution: First, we should define the important internal points as shown below:

r ( t−T o )

r ( t )

Delay, T o

x ( t ) y ( t )

2

Now we write the system equations as follows:

y ð t Þ¼ r ð t T o Þ ; r ð t Þ¼ x ð t Þ 2y ð t Þ;
) y ð t Þ¼ x ð t T o Þ 2y ð t T o Þ: